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    Diagonalizing Quadratic Bosonic Operators by Non-Autonomous Flow Equations

    Posted By: Underaglassmoon
    Diagonalizing Quadratic Bosonic Operators by Non-Autonomous Flow Equations

    Diagonalizing Quadratic Bosonic Operators by Non-Autonomous Flow Equations
    AMS | Mathematics | November 13, 2015 | ISBN-10: 1470417057 | 134 pages | pdf | 1.5 mb

    by Volker Bach, Jean-Bernard Bru
    The authors study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space.

    Abstract

    We study a non–autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. We specify assumptions that ensure the global existence of its solutions and allow us to derive its asymptotics at temporal infinity. We demonstrate that these assumptions are optimal in a suitable sense and more general than those used before. The evolution equation derives from the Brocket–Wegner flow that was proposed to diagonalize matrices and operators by a strongly continuous unitary flow. In fact, the solution of the non–linear flow equation leads to a diagonalization of Hamiltonian operators in boson quantum field theory which are quadratic in the field.

    Table of Contents

    Introduction
    Diagonalization of quadratic boson Hamiltonians
    Brocket-Wegner flow for quadratic boson operators
    Illustration of the method
    Technical proofs on the one-particle Hilbert space
    Technical proofs on the boson Fock space
    Appendix
    References

    More info and Hardcover at AMS

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